{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,24]],"date-time":"2025-08-24T01:26:03Z","timestamp":1755998763675},"reference-count":24,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Unc. Fuzz. Knowl. Based Syst."],"published-print":{"date-parts":[[2005,2]]},"abstract":"<jats:p> The aim of this paper is to o study the evolution of positive HIV population for manifestation of AIDS, the Acquired Immunodeficiency Syndrome. <\/jats:p><jats:p> For this purpose, we suggest a methodology to combine a macroscopic HIV positive population model with an individual microscopic model. The first describes the evolution of the population whereas the second the evolution of HIV in each individual of the population. This methodology is suggested by the way that experts use to conduct public policies, namely, to act at the individual level to observe and verify the manifest population. <\/jats:p><jats:p> The population model we address is a differential equation system whose transference rate from asymptomatic to symptomatic population is found through a fuzzy rule-based system. The transference rate depends on the CD4+ level, the main T lymphocyte attacked by the HIV retrovirus when it reaches the bloodstream. The microscopic model for a characteristic individual in a population is used to obtain the CD4+ level at each time instant. From the CD4+ level, its fuzzy initial value, and the macroscopic population model, we compute the fuzzy values of the proportion of asymptomatic population at each time instant t using the extension principle. Next, centroid defuzzification is used to obtain a solution that represents the number of infected individuals. This approach provides a method to find a solution of a non-autonomous differential equation from an autonomous equation, a fuzzy initial value, the extension principle, and center of gravity defuzzification. Simulation experiments show that the solution given by the method suggested in this paper fits well to AIDS population data reported in the literature. <\/jats:p>","DOI":"10.1142\/s0218488505003308","type":"journal-article","created":{"date-parts":[[2005,4,11]],"date-time":"2005-04-11T17:35:22Z","timestamp":1113240922000},"page":"39-58","source":"Crossref","is-referenced-by-count":11,"title":["METHODOLOGY TO DETERMINE THE EVOLUTION OF ASYMPTOMATIC HIV POPULATION USING FUZZY SET THEORY"],"prefix":"10.1142","volume":"13","author":[{"given":"ROSANA MOTTA","family":"JAFELICE","sequence":"first","affiliation":[{"name":"Faculty of Mathematics,  Federal University of Uberl\u00e2ndia, 38408-100 Uberl\u00e2ndia, MG, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"LA\u00c9CIO CARVALHO","family":"DE BARROS","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, IMECC, State University of Campinas, 13083-859 Campinas, SP, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"RODNEY CARLOS","family":"BASSANEZI","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics,  IMECC, State University of Campinas, 13083-859 Campinas, SP, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"FERNANDO","family":"GOMIDE","sequence":"additional","affiliation":[{"name":"Department of Computer Engineering and  Industrial Automation, FEEC, State University of Campinas, 130830-970 Campinas, SP, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,21]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1016\/S0019-9958(65)90241-X"},{"key":"rf2","volume-title":"A First Course in Fuzzy Logic","author":"Nguyen H. T.","year":"2000"},{"key":"rf3","volume-title":"Fuzzy sets and systems - Theory and applications","author":"Dubois D.","year":"1980"},{"key":"rf4","doi-asserted-by":"crossref","DOI":"10.7551\/mitpress\/3926.001.0001","volume-title":"An Introduction to Fuzzy Sets: Analysis and Design","author":"Pedrycz W.","year":"1998"},{"key":"rf5","unstructured":"E.\u00a0Sanchez, Fuzzy Automata and Decision Processes, ed. M. M.\u00a0Gupta (North-Holland, Amsterdam, 1977)\u00a0pp. 221\u2013234."},{"key":"rf6","first-page":"4","volume":"1","author":"Sanchez E.","journal-title":"Int. J. Biom. Fuzzy Systems Ass."},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1016\/S0898-1221(03)00141-X"},{"key":"rf8","unstructured":"R. M.\u00a0Jafelice, Frontiers in Artificiat Intelligence and Applications\u00a085 (IOS Press, Ohmsha, 2002)\u00a0pp. 208\u2013215."},{"key":"rf9","first-page":"1463","volume":"66","author":"Jafelice R. M.","journal-title":"Bulletin of Mathematical: Biology"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1093\/ije\/28.3.550"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1016\/S0933-3657(02)00070-2"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1016\/S0933-3657(00)00071-3"},{"key":"rf13","volume-title":"Mathematiccsl Biology","author":"Murray J.","year":"1990"},{"key":"rf14","doi-asserted-by":"crossref","DOI":"10.1007\/b98868","volume-title":"Mathematical Biology I: An Intrvduction","author":"Murray J.","year":"2002"},{"key":"rf15","doi-asserted-by":"crossref","DOI":"10.1007\/b98869","volume-title":"Mathematical Biology II: Spatial Models and Biomedical Applicatons","author":"Murray J.","year":"2003"},{"key":"rf16","first-page":"74","volume":"272","author":"Novak M.","journal-title":"Science"},{"key":"rf17","first-page":"7","volume":"7","author":"Peterman T.","journal-title":"Epidemiology Reviews"},{"key":"rf18","first-page":"589","volume":"71","author":"Caetano M.","journal-title":"Academia Brasileira de Ci\u00eancias"},{"key":"rf19","doi-asserted-by":"publisher","DOI":"10.1006\/bulm.2001.0257"},{"key":"rf20","doi-asserted-by":"publisher","DOI":"10.1137\/S0036144598335107"},{"key":"rf21","unstructured":"M.\u00a0Saag, Tratamento Cl\u00ednico da AIDS (in Portuguese), 3rd edn., eds. M.\u00a0Sande and P. A.\u00a0Volberding (Revinter, 1995)\u00a0pp. 27\u201343."},{"key":"rf22","doi-asserted-by":"publisher","DOI":"10.1142\/S0218488597000117"},{"key":"rf23","first-page":"181","volume":"5","author":"Oberguggenberger M.","journal-title":"Math. and Computer Modelling of Dynamical Systems"},{"key":"rf24","first-page":"348","author":"Mizukoshi M. T.","journal-title":"58\u00b0 Semin\u00e1rio Brasileiro de An\u00e1lise"}],"container-title":["International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218488505003308","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T17:15:57Z","timestamp":1565198157000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218488505003308"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,2]]},"references-count":24,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2011,11,21]]},"published-print":{"date-parts":[[2005,2]]}},"alternative-id":["10.1142\/S0218488505003308"],"URL":"https:\/\/doi.org\/10.1142\/s0218488505003308","relation":{},"ISSN":["0218-4885","1793-6411"],"issn-type":[{"value":"0218-4885","type":"print"},{"value":"1793-6411","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,2]]}}}